Complete Fermi–Dirac integral

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In mathematics, the complete Fermi–Dirac integral, named after Enrico Fermi and Paul Dirac, for an index is given by

F_j(x) = \frac{1}{\Gamma(j+1)} \int_0^\infty \frac{t^j}{\exp(t-x) + 1}\,dt.

This is an alternate definition of the polylogarithm function. The closed form of the function exists for j = 0:

F_0(x) = \ln(1+\exp(x)).\,

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